Finite Group Databasebeta

← C29×#8996 #20303896

Subgroups — C29×#8996 #20303896

Order 7424.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3035C211yesmaximal, characteristic
2C29×#2925C211yesmaximal, characteristic, complemented
3C29×#1492C211yesmaximal, characteristic, complemented
4C29×#1480C211yesmaximal, characteristic, complemented
5C29×#1476C211yesmaximal, characteristic, complemented
6C29×#1301C211yesmaximal, characteristic, complemented
7C29×#1277C211yesmaximal, characteristic, complemented
8C2×C29×#135—21no—
9C29×#532C2211yescharacteristic
10C4×#41×C29C2211yescharacteristic
11C29×#464—21no—
12C29×#463—21no—
13C29×#462C411yescharacteristic
14C29×#461C411yescharacteristic
15C29×#460C411yescharacteristic
16C29×#459C411yescharacteristic
17C29×#433—22no—
18C29×#432—21no—
19C29×#431—21no—
20C29×#431C2211yescharacteristic
21C29×#423C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C29×#416—21no—
25C29×#408—21no—
26C29×#405—21no—
27C2×C4×C8×C29C2211yescharacteristic
28C29×Q8⋊C8—21no—
29C29×D4⋊C8—21no—
30C29×D4⋊C8—21no—
31C29×D4⋊C8—22no—
32C29×D4⋊C8—21no—
33C2×#41×C29—21no—
34C2×#41×C29D411yescharacteristic
35C29×#135—42no—
36C29×#135—42no—
37C2×Q16×C29—21no—
38C2×SD16×C29—21no—
39C2×SD16×C29—21no—
40C2×D8×C29—21no—
41C2×M16×C29—21no—
42C22×C8×C29—21no—
43C22×C8×C29—21no—
44C22×C8×C29—21no—
45C29×C4⋊Q8C2×C411yescharacteristic
46C29×#127C2×C411yescharacteristic
47C29×#124—21no—
48C29×#121—21no—
49C29×#121—21no—
50C4×Q8×C29C2×C411yescharacteristic
51C4×Q8×C29D411yescharacteristic
52C4×D4×C29—21no—
53C4×D4×C29—21no—
54C4×D4×C29—21no—
55C4×D4×C29—21no—
56C4×D4×C29C2×C411yescharacteristic
57C4×D4×C29D411yescharacteristic
58C29×#117—21no—
59C29×#117D411yescharacteristic
60C2×C42×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8C2×C411yescharacteristic
67C29×C4⋊C8C2×C411yescharacteristic
68C29×C4⋊C8D411yescharacteristic
69C29×C4⋊C8D411yescharacteristic
70C29×C4⋊C8D412yes—
71C29×#103—21no—
72C29×#103—21no—
73C29×#102—21no—
74C29×#102—21no—
75C29×C22⋊C8—22no—
76C29×C22⋊C8—22no—
77C29×C22⋊C8—21no—
78C29×#97—22no—
79C4×C8×C29—22no—
80C4×C8×C29—21no—
81C4×C8×C29—21no—
82C4×C8×C29—21no—
83#41×C29—21no—
84#41×C29—21no—
85#41×C29—21no—
86#41×C29—21no—
87#41×C29—41no—
88#41×C29—41no—
89#41×C29—41no—
90#41×C29—41no—
91C2×Q8×C29—21no—
92C2×Q8×C29C22⋊C411yescharacteristic
93C2×D4×C29—21no—
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29—21no—
97C2×D4×C29—41no—
98C2×D4×C29C22⋊C411yescharacteristic
99C22×C4×C29—21no—
100C22×C4×C29—21no—
101C22×C4×C29—21no—
102C22×C4×C29—41no—
103C22×C4×C29C2×D411yescharacteristic
104C22×C4×C29#4111yescharacteristic
105C22×C4×C29#4111yescharacteristic
106Q16×C29—42no—
107SD16×C29—42no—
108SD16×C29—42no—
109D8×C29—42no—
110M16×C29—41no—
111M16×C29—41no—
112C2×C8×C29—22no—
113C2×C8×C29—21no—
114C2×C8×C29—21no—
115C2×C8×C29—21no—
116C2×C8×C29—21no—
117C2×C8×C29—22no—
118C2×C8×C29—41no—
119C2×C8×C29—41no—
120C2×C8×C29—41no—
121C2×C8×C29—41no—
122C2×C8×C29—41no—
123C2×C8×C29—41no—
124C2×C8×C29—41no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—21no—
128C4⋊C4×C29—21no—
129C4⋊C4×C29C22⋊C411yescharacteristic
130C4⋊C4×C29C22⋊C411yescharacteristic
131C22⋊C4×C29—21no—
132C22⋊C4×C29—21no—
133C22⋊C4×C29—21no—
134C22⋊C4×C29—41no—
135C22⋊C4×C29—41no—
136C42×C29—21no—
137C42×C29—21no—
138C42×C29—21no—
139C42×C29C22×C411yescharacteristic
140C42×C29C2×D411yescharacteristic
141C42×C29C2×D411yescharacteristic
142C42×C29C2×D411yescharacteristic
143#8996C2911yesmaximal, characteristic, direct product factor, Sylow
144C23×C29—21no—
145C23×C29—41no—
146C23×C29#12311yescharacteristic
147Q8×C29—21no—
148Q8×C29—21no—
149Q8×C29—41no—
150Q8×C29—41no—
151D4×C29—21no—
152D4×C29—21no—
153D4×C29—42no—
154D4×C29—41no—
155D4×C29—41no—
156D4×C29—41no—
157D4×C29—41no—
158D4×C29—41no—
159D4×C29—41no—
160D4×C29—81no—
161D4×C29—81no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—41no—
168C2×C4×C29—41no—
169C2×C4×C29—41no—
170C2×C4×C29—41no—
171C2×C4×C29—41no—
172C2×C4×C29—41no—
173C2×C4×C29—81no—
174C2×C4×C29—81no—
175C2×C4×C29—81no—
176C2×C4×C29C2×C22⋊C411yescharacteristic
177C2×C4×C29C4×D411yescharacteristic
178C2×C4×C29C4×D411yescharacteristic
179C2×C4×C29#12011yescharacteristic
180C2×C4×C29#12111yescharacteristic
181C2×C4×C29#12111yescharacteristic
182C2×C4×C29#13511yescharacteristic
183C2×C4×C29#13511yescharacteristic
184C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
186C8×C29—42no—
187C8×C29—41no—
188C8×C29—41no—
189C8×C29—41no—
190C8×C29—41no—
191C8×C29—42no—
192C8×C29—81no—
193#3035C2×C2911yescharacteristic
194#2925C2×C2911yescharacteristic, complemented
195#1492C2×C2911yescharacteristic, complemented
196#1480C2×C2911yescharacteristic, complemented
197#1476C2×C2911yescharacteristic, complemented
198#1301C2×C2911yescharacteristic, complemented
199#1277C2×C2911yescharacteristic, complemented
200C22×C29—21no—
201C22×C29—21no—
202C22×C29—41no—
203C22×C29—41no—
204C22×C29—41no—
205C22×C29—81no—
206C22×C29—81no—
207C22×C29—81no—
208C22×C29#38611yescharacteristic
209C22×C29#48211yescharacteristic
210C22×C29#48211yescharacteristic
211C4×C29—21no—
212C4×C29—21no—
213C4×C29—21no—
214C4×C29—41no—
215C4×C29—41no—
216C4×C29—41no—
217C4×C29—81no—
218C4×C29#41611yescharacteristic
219C4×C29#41811yescharacteristic
220C4×C29#44311yescharacteristic
221C4×C29#44411yescharacteristic
222C4×C29#44911yescharacteristic
223C4×C29#44911yescharacteristic
224C2×#135—21no—
225#532C22×C2911yescharacteristic
226C4×#41C22×C2911yescharacteristic
227#464—21no—
228#463—21no—
229#462C4×C2911yescharacteristic
230#461C4×C2911yescharacteristic
231#460C4×C2911yescharacteristic
232#459C4×C2911yescharacteristic
233#433—22no—
234#432—21no—
235#431—21no—
236#431C22×C2911yescharacteristic
237#423C22×C2911yescharacteristic
238C2×C4⋊C8C22×C2911yescharacteristic
239C2×C4⋊C8C22×C2911yescharacteristic
240#416—21no—
241#408—21no—
242#405—21no—
243C2×C4×C8C22×C2911yescharacteristic
244Q8⋊C8—21no—
245D4⋊C8—21no—
246D4⋊C8—21no—
247D4⋊C8—21no—
248D4⋊C8—22no—
249C2×C29—21no—
250C2×C29—21no—
251C2×C29—81no—
252C2×C29—161no—
253C2×C29#187511yescharacteristic
254C2×C29#187611yescharacteristic
255C2×C29#188111yescharacteristic
256C2×#41—21no—
257C2×#41D4×C2911yescharacteristic
258#135—42no—
259#135—42no—
260C2×Q16—21no—
261C2×SD16—21no—
262C2×SD16—21no—
263C2×D8—21no—
264C2×M16—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C4⋊Q8C2×C4×C2911yescharacteristic
269#127C2×C4×C2911yescharacteristic
270#124—21no—
271#121—21no—
272#121—21no—
273C4×Q8C2×C4×C2911yescharacteristic
274C4×Q8D4×C2911yescharacteristic
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4C2×C4×C2911yescharacteristic
280C4×D4D4×C2911yescharacteristic
281#117—21no—
282#117D4×C2911yescharacteristic
283C2×C42—21no—
284C2×C42C23×C2911yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8C2×C4×C2911yescharacteristic
290C4⋊C8C2×C4×C2911yescharacteristic
291C4⋊C8D4×C2911yescharacteristic
292C4⋊C8D4×C2911yescharacteristic
293C4⋊C8D4×C2912yes—
294#103—21no—
295#103—21no—
296#102—21no—
297#102—21no—
298C22⋊C8—22no—
299C22⋊C8—22no—
300C22⋊C8—21no—
301#97—22no—
302C4×C8—22no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—21no—
306C29#899611yescharacteristic, direct product factor, Sylow
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41—41no—
315C2×Q8—21no—
316C2×Q8C22⋊C4×C2911yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4C22⋊C4×C2911yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4C2×D4×C2911yescharacteristic
328C22×C4#41×C2911yescharacteristic
329C22×C4#41×C2911yescharacteristic
330Q16—42no—
331SD16—42no—
332SD16—42no—
333D8—42no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—22no—
341C2×C8—21no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4C22⋊C4×C2911yescharacteristic
354C4⋊C4C22⋊C4×C2911yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42C22×C4×C2911yescharacteristic
364C42C2×D4×C2911yescharacteristic
365C42C2×D4×C2911yescharacteristic
366C42C2×D4×C2911yescharacteristic
367C23—21no—
368C23—41no—
369C23C29×#12311yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—41no—
374D4—21no—
375D4—21no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊C4×C2911yescharacteristic
400C2×C4C4×D4×C2911yescharacteristic
401C2×C4C4×D4×C2911yescharacteristic
402C2×C4C29×#12011yescharacteristic
403C2×C4C29×#12111yescharacteristic
404C2×C4C29×#12111yescharacteristic
405C2×C4C29×#13511yescharacteristic
406C2×C4C29×#13511yescharacteristic
407C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
408C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
409C8—42no—
410C8—41no—
411C8—41no—
412C8—42no—
413C8—41no—
414C8—41no—
415C8—81no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22C29×#38611yescharacteristic
425C22C29×#48211yescharacteristic
426C22C29×#48211yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4C29×#41611yescharacteristic
435C4C29×#41811yescharacteristic
436C4C29×#44311yescharacteristic
437C4C29×#44411yescharacteristic
438C4C29×#44911yescharacteristic
439C4C29×#44911yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—161no—
444C2C29×#187511yescharacteristic
445C2C29×#187611yescharacteristic
446C2C29×#188111yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C29×#2925C2semidirect
3. C29×#1492C2semidirect
4. C29×#1480C2semidirect
5. C29×#1476C2semidirect
6. C29×#1301C2semidirect
7. C29×#1277C2semidirect
143. #8996C29direct (N × H)
194. #2925C2×C29semidirect
195. #1492C2×C29semidirect
196. #1480C2×C29semidirect
197. #1476C2×C29semidirect
198. #1301C2×C29semidirect
199. #1277C2×C29semidirect
306. C29#8996direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C29×#30352
C29×#29252
C29×#14922
C29×#14802
C29×#14762
C29×#13012
C29×#12772
#899629